I am stumped please help me with this problem. ----

A man was walking down a path one day when a women appeared in front of it at exactly 8:06 AM.
The next day, the man was walking down the same path, and the women appeared in front of it at 6:03 PM. The next day, the same thing happened at 11:05 AM. The next three days were at 3:09 PM, 5:05 AM, and 4:01 AM. What time did the woman appear in front of the man on the 7th day.

Since he sees this woman whenever he takes a walk, the time he sees her next depends upon his own unpredictable behavior. Perhaps he rested on the seventh day.